### Find the standard equation of the sphere.

### Let P1 = (-7, -9, 7) and P2 = (0, 1, 1) be endpoints of a diameter

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Show Work Step by Step on your TI-89 Calculator Screen

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Hello, everystepcalculus.com. A problem regarding Shell Method and the axis of rotation is vertical. A Yahoo problem. Let’s do it. Index 8to get to my menu. You need to get to the s’s of the alphabet so you have to go down to the bottom of the alphabet by going up and then clicking up to go to finding shell. And it is there. And we have the choice of horizontal axis or vertical axis, we want this problem is vertical axis. There’s the formula. And it’s taken me a long time to program this stuff, but if (p)x is the radius, if it’s not given enter x for p(x), okay, cause there’s two functions, p(x) and h(x). And sometimes it’s more elaborate than this one is. You have to press alpha before you enter anything into these entry lines so I’m gonna…. here’s p(x) here, alpha x I’m gonna enter. And for h(x) is the problem, alpha 6 minus x. 1Oops. 6 minus X. I always show you what you’ve entered you can change it if you want, that’s okay, now, I press number one. One of the tough things about shell is the confusion of the whole thing, and the nonsense of the whole thing, but then we’re gonna find the A&B limits. You do that by– if nothing else is given for the x value, than the x is equal to 0 because you got a vertical axis of revolution. It’s vertical, and we set the X at equals zero point. So we set the equation equal to that. 0 equals 6 minus x, we get the limits, it’s six. This is where the function crosses the x-axis. So, here’s the equation now for the integral. And so we have this issue. Mark this on your paper.

When we do the integration, here’s the integration of the function. And, as we substitute at x equals 6, the limits, it’s 72 pi and x=0,. we get 0. Upper limit minus lower is 72 pi.Have a good one.

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Hello, everyone. This is Tom from everystepcalculus.com. There’s been many, there’s always requests for Integral Calculator with Steps and that’s exactly what my programs do. And Integration is one of the toughest things in Calculus. It was for me when I was in class. I hated Calculus. You probably feel the same way and I’ve found nobody that likes Calculus. Except maybe Professors. But anyways, I’m going to show you how my programs work on U Substitution. Index 8 to get to my menu. I’m already at U Substitution. I have scrolled there. We’re going to enter our function. You have to press Alpha before you enter anything into these entry lines, here. Alpha 6 times x to the fourth power times the quantity parentheses 3 times x to the fifth power plus 2, close off the parentheses to the sixth power. I always show you what you’ve entered. 6x 4 times 3 x quantative to the 5 plus 2 to 6. Looks

good to me. I say it’s okay. And we’re going to work the problem. Busy means the program is loading. We’re going to evaluate this. First we rewrite it where all constants come out of the integral. And then we put the x to the 4. The way that you know that any problem is U Substitution is that you look immediately at what’s inside the parentheses. You take the derivative, right now you should be able to do, this is 15x to the 4. Right now in one second, you should be able to know the derivative of that. And you notice that x4 is on the outside, too. If it isn’t, it’s not a U Substitution problem. It has to be converted, okay. So I do all that for you, really. But that you have some understanding of how you do U Substitution. U is equal to this, du is equal to this and then we make this the other trick, this whole system here took me about a year to figure this out in a system that works, you know. And so, this always has to be x to the 4 dx over here so you have to take the 15 and divide the du by that on the other side using Algebra, of course. And so it works the problem. 6, you take of course the du with the 6 here, you have a du with a 15 notice the 15 come out of the, here’s the constant again so that comes out of the integral and goes in front right here, see it right here. 6 times that, of course, with the 2 fifths. etc, etc. Here’s the answer to your problem right here. Have a good one. everystepcalculus.com

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Hello, everyone. This is Tom from everystepcalculus.com, everystepphysics.com. I’m going to do a integral of a natural log in this video to go with my menu. Let’s do an index 8 to get to my menu. I’m already at LN of X integral, which is natural log of you know, and integrate that. We’re going to press number 2, integration. And we’re going to integrate transcendentals. Number 1, log of X. And you have to press alpha before you enter anything in these entry lines here. And we’re going to enter the function that you see. Alpha 2nd log of 5 times X. It will show you what you’ve entered; you can change it if you want. I say it’s okay. I’m going to rewrite this. Like you see, integral of log of 5x and then we have the 1 over here, DX, to show you that we’re going to do DV is equal to 1, V is equal to the interval of 1dx. The answer is X. And then U is log of 5x, but that always equals the derivative of that is one over X. Here’s the formula: VU minus the integral of VDU. And we plug in the variables for the formula. Here’s V and here’s U, minus the integral of V again and then DU. And then we’re going to integrate 1 here, because that’s what that works out to, what we just put down before. And so the integration of integral of 1 is minus X. So here’s the answer: X times log of 5 times X minus 1 plus C. Notice we’ve factored the X out here. Also notice that sometimes‚ you might think about this too‚ log of 5 times X is really log of 5 plus log of X, so that could be written like that, too. X times log of 5 times log of X minus 1 plus C. So subscribe at my site and you can see more movies that I might make for your enjoyment. Have a good one.

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Hello again; Tom from everystepcalculus.com, everystepphysics.com. I’m going to do a line integral in calculus 3 physics. This is right off of Paul’s notes, his example. You can check if you Google line integral. None of us are interested in line integrals; all we want to do is know how to do the problem to pass a quiz or a midterm. Very difficult. I’ve tried to find what does a line integral represent. In other words, what’s the SI units for the answer that they get, and I can’t find it. So that shows you something about calculus. To me, most of it is nonsense. Index 8 to get to my menu. I’m going to scroll down to line integral. I’m already there to save time. And we’re not in a vector field we’re given the RT situation. And I show you the formula; this here is the formula: RT times the magnitude of R of the derivative of RT. And then this worked out. This is RT here, and then the magnitude absolute value of R, derivative of RT is this. Write this all down in your paper, exactly as you see it so you look like you know what you’re doing. And we’re going to put the RT was given in this a problem. We’re going to do alpha before you enter anything into these entry lines here, alpha 4 times 2nd cosign of T alpha 4 times 2nd sign of T. And when they don’t give you the Z, you just put 0 in. Alpha 0. Now it will show you what you’ve entered; you can change it if you want. I say it’s okay. Now we start working out the‚this is a vector here when you have these arrows on these sides, it’s called a vector, RT vector. We’re doing the derivative of that, which equals minus 4 sign of T and 4 cosign of T, et cetera. And we do the magnitude, which is squaring those derivatives. And the answer turns out to be the square root of 16, which is 4, really. And then we’re going to enter the function given, which is alpha X times Y to the fourth power. Where they dream up all these nonsense formulas and functions is unbelievable in calculus. I say it’s okay; you could have changed that if you want. So for the range of alpha, minus pi divided by 2 to the range of alpha pi positive divided by 2. So here we have the range, and here we have the function, and here we have the derivative magnitude of the derivative of RT function. And you do the calculation just as you see them here on your paper. Over the range of this here, you’ve already done the derivative here. Here’s the derivative of that. The answer is 8192 over 5. Notice now it’s just an arbitrary number. We’d like to know area or something, distance, or length or something, but it’s just a number. So you have to decide yourself how important that is. I mean, to me, how important is the slope of a line, which is the derivative or the area under curves, or volume under functions, under spheres and stuff. Have a good one. Go to my site, subscribe and you can see more movies that I might make.

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Hello, Tom from everystepcalculus.com, everystepphysics.com. Don’t forget physics, either, in your schooling. I‚m going to do two problems in calculus: a definite integral, and a log problem. I’ll show you the diversity of my programs. And my programs turn the titanium into a calculus calculator with steps. A calculus calculator with steps‚ that’s exactly what my programs do. So let’s do it. Index 8 to get to my main menu. We’re going to scroll down to definite integral in the D’s. Definite integral in X because you only see X in the problem, right? We’re going to enter the function. You have to press alpha before you enter anything into these entry lines. You’re going to press alpha, and we‚re going to enter the function. 3 minus X to the cubed plus 4 times X. Now we show you what you’ve entered; you can change it if you want. I say it’s okay. I’m going to enter the range. Lower range is alpha minus 2. Upper range is alpha 2. I say that’s okay also. And we integrate it, which is this right here. We’ve integrated each one of those terms, separated by plus or minus signs. And at the upper range, X equals 2. You add these into the‚ you’re going to use, instead of quotation marks, you’re going to use parentheses around your additions into the main function. But it equals 10. And if X equals minus 2, the answer is minus 2. Upper minus lower is equal to 12 square units. Pretty neat, huh? All right, we’re going to go back to the main menu. Number two: And we’re going to scroll down. Now this is in the L section, logs. So I’m going to do this quick. Behind the simulator here I can only use, I only have one essential finger to do this with. On your calculator, the titanium, you can hold the 2nd down with your thumb or finger and press this. It’ll go screen by screen and really go quick down to logs. We have natural logs and all kinds diversity in my menus. I’ve done all the calculus problems, or most of the tests, of course. Nobody can do all of the calculus problems; there’s millions of derivations of that. Log problems, okay. We’re going to evaluate this log problem, number 3. We have to press 2nd alpha to get to the letter register to put log in. We’re going to enter the problem. We want to make, we have 2nd down here, but we want to turn it to black like that. Then we can put the logs in there, so that’s‚Äî The letters appear over the numbers, you can see them. And then we’re going to go back to numbers, which erases that black mark there, indication. And we’re going to put 3 parentheses 1 divided by 27. Close off the parenthesis. And I show you what you’ve entered. It looks pretty good to me. We’re going to press 1, and here’s the answer step-by-step. In other words, if you on your calculator, if you put 3 to the exponent minus 3, you’re going to come up with 127. All right. Pretty neat, huh? Everystepcalculus.com. Go to my site. Buy my program if you want to pass calculus or physics. Or subscribe so you can see more videos. Have a good one.

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Hello everyone; Tom from everystepcalculus.com and everystepphysics.com. Don’t forget physics. I have turned through the use of my programs, or for programming, your titanium calculator into an implicit differentiation calculator with steps. And that’s exactly what my programs do. So let’s do it. Index8() to get to my menu. I’m already at implicit differentiation. I’ve scrolled there. On your titanium, if you want to go to my menu and go down quickly, you hold the 2nd button down here and then use the down cursor here. We’re already at that, so. And then enter the function. You have to press alpha before you enter anything in these entry lines here. And the problem is alpha Y squared plus 3 times X minus 8 times Y plus 3 equals 0. Now it will show you what you’ve entered, and you change it if you want. I say it’s okay. You’re differentiating all of the terms on both sides of the equals sign. You must have a 0 or a constant on the right of the equals sign. You have to use the algebra to make that happen if they give you a more difficult problem, or a different look at a problem. And so we differentiate each one of the terms. I do that for you; you write this on your paper as we go through it, exactly as you see it here. And we combine the DY DX terms, separate it from the other terms, and here’s the answer right here. Now we want to evaluate it at a point, so we’re going to press the X value is alpha 4 and alpha 3. I show you that also; it looks good to me. So we’re substituting 4 and 3 for the X and the Y values and then find the derivative. Cut them to one half and the slope of the line is 333 degrees. That means that the slope is going to be here’s 360 going this way. Here’s 270 going down. So the slope is going to be like this. Pretty neat, huh? Everystepcalculus.com. Go to my site. Buy my programs if you want help passing calculus. Or subscribe to enjoy more videos that I might make. Have a good one.

Implicit Differentiation test question solved by TI-89

Implicit Differentiation calculator – Video Example #2

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Hello, Tom from everystepcalculus.com, everystepphysics.com. Don’t forget physics, either, in your schooling. I’m going to do two problems in calculus: a definite integral, and a log problem. I’ll show you the diversity of my programs. And my programs turn the titanium into a calculus calculator with steps. A calculus calculator with steps, that’s exactly what my programs do. So let’s do it. Index 8 to get to my main menu. We’re going to scroll down to definite integral in the D’s. Definite integral in X because you only see X in the problem, right? We’re going to enter the function. You have to press alpha before you enter anything into these entry lines. You’re going to press alpha, and we’re going to enter the function. 3 minus X to the cubed plus 4 times X. Now we show you what you’ve entered; you can change it if you want. I say it’s okay. I’m going to enter the range. Lower range is alpha minus 2. Upper range is alpha 2.

I say that’s okay also. And we integrate it, which is this right here. We’ve integrated each one of those terms, separated by plus or minus signs. And at the upper range, X equals 2. You add these into the you’re going to use, instead of quotation marks, you’re going to use parentheses around your additions into the main function. But it equals 10. And if X equals minus 2, the answer is minus 2. Upper minus lower is equal to 12 square

units. Pretty neat, huh? All right, we’re going to go back to the main menu. Number two: And we’re going to scroll down. Now this is in the L section, logs. So I’m going to do this quick. Behind the simulator here I can only use, I only have one essential finger to do this with. On your calculator, the titanium, you can hold the 2nd down with your thumb or finger and press this. It’ll go screen by screen and really go quick down

to logs. We have natural logs and all kinds diversity in my menus. I’ve done all the calculus problems, or most of the tests, of course. Nobody can do all of the calculus problems; there’s millions of derivations of that. Log problems, okay. We’re going to evaluate this log problem, number 3. We have to press 2nd alpha to get to the letter register to put log in. We’re going to enter the problem. We want to make, we have 2nd down here, but

we want to turn it to black like that. Then we can put the logs in there, so that’s—The letters appear over the numbers, you can see them. And then we’re going to go back to numbers, which erases that black mark there, indication. And we’re going to put 3 parentheses 1 divided by 27. Close off the parenthesis. And I show you what you’ve entered. It looks pretty good to me. We’re going to press 1, and here’s the answer step-by-step. In other words, if you on your calculator, if you put 3 to the exponent minus 3, you’re going to come up with 127. All right. Pretty neat, huh? Everystepcalculus.com. Go to my site. Buy my program if you want to pass calculus or physics. Or subscribe so you can see more videos. Have a good one.

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Hello Tom from EveryStepCalculus.com EveryStepPhysics.com there’s been many searches for ti-89 partial fractions and I’m going to show you how that works on your titanium.

You can download these programs into your titanium and do this exactly like I do it here a miracle of programming from the inventors MIT the geniuses over there. So I’m going to show you index8() to get to my menu. I’m already at partial fractions which you would scroll to when you know the title of what you’re looking for in calculus.

And we’re gonna enter the integral and that is quite long but I’m going to do it yet to press alpha before you enter anything in these entry lines here. Alpha left parenthesis 2 times X cubed minus 4 times x squared minus 15 times X plus 5 close off the parentheses.

Divide sign more parentheses x squared minus 2 times X minus 8. Remember calculus is the sudoko math in my opinion a lot of nonsense and this is, this is certainly true of partial fractions. Now you try this without a program, you can do it if you want, not me. Press ENTER, when it’s busy you’re loading the program I always show you what you’ve entered so you can change it if you want to X cubed minus 4x squared minus 15 X plus 5.

That’s crew x squared minus 2x minus 8 that’s good, let’s say ok, and so let’s do it. First thing you do is factor the denominator here, it’s loading programs again but once it’s loaded it’s quick on your calculator but these are long programs. Because the numerator is higher than or equal to then than the denominator you have to use short division.

So 2x cubed divided by x squared is 2x and that’ll be added to the answer at the end. This is a quotient that’ll be added to the answer at the end, calculator is computing and you write all this on your paper of course. A X minus 4 B X plus 2 times the factored denominator and you get this. Write this stuff down, I’m not going to explain it to you, and x equals -2 it equals this here x equals 4. We’re solving for all the a B’s and C’s equals 1/2 and x equals 4 I do that for you amazing program.

I think a equals 3 2 3 and 3 halves here’s the answer, 3 halves over X minus 4 plus minus 1/2 over X plus 2 plus. Here’s the quotient we found with short division plus C and then we even do the integrals for you remember most of these are logs because when you have something on a denominator without an exponent it has to be a log problem. It has to be a log differentiation.

So good luck in your calculus class and subscribe to me, maybe see more videos or you can actually buy the programs and enjoy passing calculus. Have a good one.

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Hello, Tom from everystepcalculus.com and everystepphysics.com. This is a problem from a student regarding Transcendental Integrations. And it involves sin. So, I’m going to show you how my programs do that. Index eight to get to the menu, main menu. I’m already scrolled to integration by parts. Generally they give you that in the problem, in a test or. I’m gonna choose sin here because that’s what the problem is. You can see the problem on your screen. And we enter the problem, here. We have to press alpha before you enter anything in these entry lines in my programs Alpha X times second sin 2 times x. I always show you what you’ve entered, you can change it if you want. Just a little bit

of teaching which I don’t really do in my programs. I show rather than teach. Professors teach and then test on mechanics. I like to show the mechanics because that’s what I needed to pass my classes. So, why is this different? Why is this integration by parts and not U Substitution? Okay well get used to memorizing the derivative of anything inside of function Right away. For instance, like this sin of 2 X here is the derivative of that is 2 times the cosine of 2 x divided, oh no it’s not divided by it’s just a it’s just a 2 times the cosine of x. Well you notice there’s no X there, okay. There has to be an x because it has to match in U Substitution. This x and this DX here. Okay. So all we get here would be 2 DX

and so there’s no X involved in the derivative of this here. Therefore you can’t use U Substitution. So it’s integration by parts which is a different formula so I’m going to keep going and I’ll show. say it’s okay. Integration by parts, you come up DV which is the already the derivative of the sin of 2x and then you’re going to integrate that to get

minus cosine of 2x divided by 2, okay. And then U is equal to X and DU, the derivative of that is 1 DX. So now we do in the formula. vu minus the integral vdu dx, etc. Write all this entire paper exactly as you see it. And you’ll get a hundred percent here’s exactly this step by steps. And the answer is here. Careful now because like for instance minus x cosine of 2x divided by 2, a lot the calculator will come up with line here and do the denominator

by 2 you know and this will have the a line and the denominator is 4. So be hip to that when you’re looking at that because this is exactly the problem. Correct, right here. Alright, have a good one.

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